A skicross-race is done in heats of four. The two fastest in each heat advance to the next level.
First the athletes do a time qualification or seeding run, one rider at a time. The 16 or 32 fastest riders advance to final heats. During the Olympics 32 ladies qualify. The qualification placement determines what heat you're in, color of bib and who gets priority to select start gate first. 1st: Red 2nd: Green 3rd: Blue 4th: Yellow
The final heats start with 8th-finals, the two fastest in each advance to quarterfinals followed by semifinals. In the semifinals the two fastest in each advance to the big final, where they race for position 1-4. The third and fourth in each semifinal advance to the small final, where they race for position 5-8.
A few days before the race the athletes are allowed training runs, all riders get the same amount of training runs. This is for safety since a skicross course is fast and contains large jumps and other features.
Some rules: you are not permitted to wilfully obstruct an opponent- no pushing, grabbing of clothes, blocking. Not adhering to these rules may result in a warning or yellow card. Shoulder to shoulder racing is allowed and happens frequently.